ANALYTICAL MODELING OF ROCK/FILL MASS INTERFACE INTERACTION AND ITS ENGINEERING APPLICATION

PRESENTED BY: TROY SMITH

IN SHIK PARK

ZHEQING HE

XIAO WEN MA

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SUPERVISOR: DR. LIANG CUI

OBJECTIVE

Develop an analytical model to predict the vertical stress considering arching effect in a stope filled with Cemented paste backfill

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OUTLINE�

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• General Information
• Literature Review
• 2D Analytical Model
• Effect of Modelo Parameters on Vertical Stress
• Engineering Application: Cost Analysis
• Conclusion and Recommendations

WHAT IS MINING?

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(Mining Lifce, 2014)

(Mining Lifce, 2014)

MINING PROCESS

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Rock Mass

Stope

Ore

Processing

Raw Material

Tailings

Cemented Paste Backfill (CPB)

Water & Binder

Transported and placed back in the stope

Mined

15 ~ 30%

70% ~ 85%

(Tailings Consultants)

TAILINGS

• Material left over after extracting  ore

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(Cook Inlet Region, Inc., 2014)

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• Returning them to the original void from which they were extracted

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• Financial and environmental benefits

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BINDER CONTENT

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(Doherty 2015)

MATERIAL PROPERTIES�

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ADHESION COHESION

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INTERNAL ANGLE OF FRICTION�(DIRECT SHEAR TEST)

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(Brainkart, 2016)

INTERNAL ANGLE OF FRICTION�(TRIAXIAL TEST)�

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(Shosha)

CURING TIME

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(Fall and Nasir, 2010)

ARCHING EFFECT

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(Terzaghi, 1943)

PROBLEM?

Three main problems to be solved with CPB

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• Mechanical Stability
• Environmentally Friendly
• Economically feasible

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MECHANICAL STABILITY

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Belem and Benzaazoua (2007)

ENVIRONMENTAL IMPACT

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Block Caving (2014)

Mining, MDA Corperation

ENVIRONMENTAL IMPACT

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A look at ways of controlling tailings to avoid future liability, Leo C. Botham 

Red Sludge From Brazilian Dam Collapse Reaches the Atlantic, Alan Taylor 

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ECONOMIC FEASIBILITY

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97-92% by weight

3-8% by weight

70-80% of Total Cost

Water

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Tailings

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CPB

METHODOLOGY

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Vertical Stress * FS = Uniaxial Compression Strength

OUTLINE�

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• General Information
• Literature Review
• 2D Analytical Model
• Effect of Modelo Parameters on Vertical Stress
• Engineering Application: Cost Analysis
• Conclusion and Recommendations

FIELD STUDY

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(RST Instruments Ltd. , 2017)

FIELD STUDY

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(Matthew et al., 2010)

MODELS

• Analytical model

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• Multiphysics model  - THMC process

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Thermal

Process

Hydraulic

Process

Mechanical

Process

Chemical

Process

Volume changes:

Heat transfer

Seepage behavior

Mechanical deformation

Binder hydration

COMPARISON

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COMPARISON – sample equations

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Multiphysics method:

Analytical method:

OUTLINE�

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• General Information
• Literature Review
• 2D Analytical Model
• Effect of Modelo Parameters on Vertical Stress
• Engineering Application: Cost Analysis
• Conclusion and Recommendations

ASSUMPTION 1

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Geometric factors are neglected.

Perfectly Rectangle

ASSUMPTION 2

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Poisson’s effect is NOT considered.

ASSUMPTION 3

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Surface of the interface between CPB & Rock is PERFECTLY FLAT.

ASSUMPTION 4

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Vertical stress along the width at the identical depth was considered to be UNIFORMLY distributed.

ASSUMPTION 5

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CPB and surrounding rock mass was considered to be HOMOGENEOUS, and ISOTROPIC materials.

ASSUMPTION 6

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Horizontal stress was considered to be only produced by the vertical stress caused by the self-weight.

ASSUMPTION 7

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Lateral Pressure Coefficient

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1. At Rest Condition

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• Active Condition

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• Passive Condition

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ASSUMPTION 7 (CONT.)

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ASSUMPTION 7 (CONT.)

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ASSUMPTION 7 (CONT.)

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ASSUMPTION 7 (CONT.)

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ASSUMPTION 8

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Mohr-Coulomb failure criterion was considered to be valid for model derivation.

IDEALIZED DIAGRAM

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FBD

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DERIVATION OF VERTICAL STRESS

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DERIVATION OF VERTICAL STRESS

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VERTICAL STRESS COMPONENTS�(BODY FORCE)

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VERTICAL STRESS COMPONENTS�(SHEAR FORCE)

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VERTICAL STRESS COMPONENTS�(ADHESIVE FORCE)

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VERTICAL STRESS COMPONENTS�(VERTICAL FORCE EQUILIBRIUM)

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VERTICAL STRESS COMPONENTS�(FINDING SOLUTION OF ODE)

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VERTICAL STRESS COMPONENTS�(FINAL CLOSED-FORM SOLUTION)

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COMPARISON OF SELF WEIGHT AND TOTAL VERTICAL STRESS

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Self-weight stress:

The total vertical stress considering arching effect:

COMPARISON OF SELF WEIGHT AND TOTAL VERTICAL STRESS

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OUTLINE�

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• General Information
• Literature Review
• 2D Analytical Model
• Effect of Modelo Parameters on Vertical Stress
• Engineering Application: Cost Analysis
• Conclusion and Recommendations

RANGES OF VALUES

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(Nasir and Fall, 2008) (Adajar and Pabilona, 2017) (Veenstra, 2013) 

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EFFECT OF ROCK/FILL MASS INTERFACE PROPERTIES

• Adhesion
• CPB Friction Angle
• CPB/Rock Friction Angle
• Stope Width
• CPB Fill Density

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PARTIAL DERIVATIVES WITH RESPECT TO EACH MODEL PARAMETERS

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PARTIAL DERIVATIVES WITH RESPECT TO EACH MODEL PARAMETERS (CONT’D)

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EFFECT OF ROCK/FILL MASS INTERFACE PROPERTIES (CONT.)

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• Adhesion

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Increase of adhesion

Reduces vertical stress & Increases arching effect

EFFECT OF ROCK/FILL MASS INTERFACE PROPERTIES (CONT.)

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• CPB Friction Angle

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Increase of CPB Friction Angle

Increases vertical stress & Reduces arching effect

EFFECT OF ROCK/FILL MASS INTERFACE PROPERTIES (CONT.)

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• CPB/ROCK Friction Angle

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Increase of CPB/Rock Friction Angle

Reduces vertical stress &

Increases arching effect

EFFECT OF ROCK/FILL MASS INTERFACE PROPERTIES (CONT.)

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• Stope Width

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Increase of stope width

Increases vertical stress &

Reduces arching effect

EFFECT OF ROCK/FILL MASS INTERFACE PROPERTIES (CONT.)

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• CPB Fill Density

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Increase of CPB Fill Density

Increases vertical stress &

Reduces arching effect

OUTLINE�

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• General Information
• Literature Review
• 2D Analytical Model
• Effect of Modelo Parameters on Vertical Stress
• Engineering Application: Cost Analysis
• Conclusion and Recommendations

COST ANALYSIS

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COST ANALYSIS (CONT.)

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Relate UCS Strength to the Binder Content

COST ANALYSIS (CONT.)

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UCS = 11.333x² + 3x+ 60

COST ANALYSIS (CONT.)

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COST ANALYSIS (CONT.)

• 𝜎𝑣𝐹𝑆=𝑈𝐶𝑆 
• 𝜎𝑣𝐹𝑆= 11.333x² + 3x+ 60
• 533𝑘𝑁𝑚²∗1.5= 11.333x² + 3x+ 60

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COMPARISON

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OUTLINE�

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• General Information
• Literature Review
• 2D Analytical Model
• Effect of Modelo Parameters on Vertical Stress
• Engineering Application: Cost Analysis
• Conclusion and Recommendations

CONCLUSION

• Mechanical Stability
• Positive Environmental Impact
• Economically Feasible
• Analytical Model over Multi-Physics
• Derive Equation
• Verify Equation
• Cheaper than Traditional Method

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REFERENCE

• A look at ways of controlling tailings to avoid future liability, Leo C. Botham, Dec 1, 2015 
• Belem, T., and Benzaazoua, M. 2008. Design and Analysis of underground Mine Paste Backfill Technology. Geotechnical and Geological Engineering, 26(2), pp 147-174.
• Block Caving (2014), http://www.groundtruthtrekking.org/Issues/MetalsMining/block-caving-underground-mining-method.html
• http://www.brainkart.com/article/Laboratory-determination-of-shear-parameters--Direct-shear-test_3475/
• http://www.ciri.com/between-hard-rock-and-a-hard-place/
• Fall, M., and Nasir, O. 2010. Mechanical Behaviour of the Interface Between Cemented Tailings Backfill and Retaining Structures Under Shear Loads. Springer Science Business Media B.V.
• Mining, MDA Coperation, https://mdacorporation.com/geospatial/international/markets/mining
• Red Sludge From Brazilian Dam Collapse Reaches the Atlantic, Alan Taylor, Nov. 24, 2015. 
• Terzaghi, K. 1943. Theoretical Soil Mechanics. John Wiley & Sons. Ney York, NY.
• https://www.rstinstruments.com/Vibrating-Wire-NATM-Stress-Cell.html
• https://mininglifeonline.net/news_view_3013.html
• HTTP://WWW.TAILINGS.INFO/STORAGE/BACKFILL.HTM

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